Cinema's presence at the London Olympics stretches beyond the spectacle of Danny Boyle's opening ceremony.

Cinema has a significant presence at the London Olympics, and not only because it is a film director, Danny Boyle, who will go down in history as the first Briton to take home gold from the games. Let it not concern us that his medal is theoretical, and made of large quantities of acclaim, adoration and gratitude, which are more precious than mere metals, not to mention easier to get through customs. It is no small feat that Boyle produced an emphatic spectacle out of that most inauspicious furnace: seven years of public dread more consistent with the approach of a second ice age. His achievement doesn’t diminish the cost of the games, or the scepticism over the supposed legacy, but it is still a miracle in its own right.

The opening ceremony was also steeped in the cinematic. The montage (preliminary list here) of British cinema in the middle of proceedings was persuasive and eccentric: we got excerpts from Oliver Twist, Kes, Gregory’s Girl, The Full Monty and Four Weddings and a Funeral, while the oddness of seeing David Bowie in The Man Who Fell to Earth was unexpectedly exhilarating. (It was sweet of Boyle, a self-professed Nicolas Roeg fan, to give that director the largest audience he’s ever had.) I was glad, too, that the famously humble Boyle included clips from his own Trainspotting, even if he stopped short of featuring the full version of the toilet scene.

Earlier in the show we were treated to a blast of the theme tune from The Archers, and the film montage went on to include those other Archers, Powell and Pressburger, in the form of A Matter of Life and Death. Mike Oldfield played several minutes of Tubular Bells, a work now forever associated with The Exorcist, and multiple Mary Poppinses filled the air. Cinema was integrated into the ceremony’s cheekiest filmed segments, with Rowan Atkinson infiltrating Chariots of Fire and the Queen joining Daniel Craig to provide a literal interpretation of the title of the next James Bond film (Skyfall). It all added up to the greatest Danny Boyle movie never made.

Four short films were also commissioned by Channel 4 and the BBC as part of the London 2012 festival. After being unveiled in June at the Edinburgh Film Festival, the shorts have received cinema and television screenings and are on the BBC iPlayer for the next few days. The most conventional offering is What If (available until 31 July) a fantasy set on a London housing estate where a young boy is helped by a guardian angel (Noel Clarke) to see his life, his surroundings and his potential future through the prism of Kipling’s poem “If.” The directing team of Max Giwa and Dania Pasquina, who have a couple of Streetdance films to their name, opt for a glossy poverty-chic look where the monochrome sleekness of La Haine gives way in moments of special hope to bursts of sentimental colour (a pot of yellow flowers, or a rainbow arching over London) à la The Wizard of Oz or Rumble Fish. It’s a well-meaning piece that smacks of an ad agency show-reel.

Mike Leigh’s contribution, A Running Jump (available until 3 August), has been described by the director himself as “a bundle of gags” and “a humorous anecdote.” This story of a manic second-hand car salesman, Perry (Eddie Marsan), trying to flog a clapped-out banger has the vivid colours and perkiness of Leigh’s ostentatiously upbeat Happy-Go-Lucky, but rather less in the way of originality. Have wacky yoga routines and fast-talking wide boys ever been funny? I’m not convinced. But Marsan has some choice moments, particularly when trying to convince his daughter to do him a favour by bombarding her with promises plucked from the air (“I’ll buy you a new pair of trainers… I’ll run you a nice hot bath… I’ll give you twenty quid…”).

Leigh is correct: the film is a sketch, a fancy. But it’s still weirdly taxing: I didn’t have nearly as much fun as the actors seemed to. And the chirpy-cheeky score, with brass and bongo drums urging us on to enjoy ourselves, has now replaced for me the yuppie landlord from Naked as the single most irritating element in any Mike Leigh film. At least A Running Jump has a majestic sign-off shot: a broken-down car spewing smoke with London spread out in the distance. A harbinger of the UK’s Olympic prospects?

It has been noted that this is the first helicopter shot Leigh has used in more than 40 years of filmmaking. Asif Kapadia’s The Odyssey, on the other hand, is comprised of little else. This short documentary (showing until 1 August) is an overview of London’s fortunes from 6 July 2005, when the city’s successful Olympic bid was announced, to the present day; special emphasis is given to the 7/7 bombings, the financial crisis and last summer’s riots, with the tone of cautious optimism captured by audio-only interviews with contributors including Robert Elms and Richard Williams. The predominance of aerial footage, with its associations of objectivity but also surveillance, gives The Odyssey a helpfully analytical tone that was sometimes missing from the same director’s feature-length documentary Senna. The images from the riots are used particularly well: the camera hovers high above the flames, keeping us at arm’s length, while the soundtrack engages intimately with the panic and the rage on the streets.

It’s hardly a surprise that the most impressive and adventurous of the four films comes from Lynne Ramsay, an acknowledged master of the short. In Swimmer (available to watch until 3 August), Ramsay uses an aural and visual collage effect to portray an angelic young man’s long swim through the wilderness. As with Kapadia’s film, the most powerful effects here are often achieved by the friction between sound and image. While the eyes are soothed and stimulated by Natasha Braier’s lyrical black-and-white cinematography, the ears are greeted with a mini-tour through British cinema, including snatches of scenes from Billy Liar, If…, The Loneliness of the Long Distance Runner and Walkabout (Roeg again).

The worst aspect of the public experience during the games is likely to be the attempt to police vigorously what we can see or hear as we move around London. The walk across the bridge to the Olympic park, for instance, has now been comprehensively spoiled, with sponsor posters obscuring the bridge’s glass panels, which previously looked out onto Stratford’s criss-crossing train tracks and Anish Kapoor’s gloriously jumbled sculpture beyond. Inching across the bridge today is a claustrophobic experience: the exterior has been rendered interior, shutting out the beautifully grimy east London mishmash. The best creative works, whether they are as vast and ambitious as Boyle’s opening ceremony or as intimate as Swimmer, travel in the opposite direction, reaching beyond physical constraints and into the limitless imagination.

Ryan Gilbey is the New Statesman's film critic. He is also the author of It Don't Worry Me (Faber), about 1970s US cinema, and a study of Groundhog Day in the "Modern Classics" series (BFI Publishing). He was named reviewer of the year in the 2007 Press Gazette awards.